Artificially structured materials such as metamaterials can extend the electromagnetic properties of conventional materials and can provide novel electromagnetic responses that may be difficult to achieve in conventional materials. Metamaterials can realize complex anisotropies and/or gradients of electromagnetic parameters (such as permittivity, permeability, refractive index, and wave impedance), whereby to implement electromagnetic devices such as invisibility cloaks (see, for example, J. Pendry et al, “Electromagnetic cloaking method,” U.S. patent application Ser. No. 11/459,728, herein incorporated by reference) and GRIN lenses (see, for example, D. R Smith et al, “Metamaterials,” U.S. patent application Ser. No. 11/658,358, herein incorporated by reference). Further, it is possible to engineer metamaterials to have negative permittivity and/or negative permeability, e.g. to provide a negatively refractive medium or an indefinite medium (i.e. having tensor-indefinite permittivity and/or permeability; see, for example, D. R. Smith et al, “Indefinite materials,” U.S. patent application Ser. No. 10/525,191, herein incorporated by reference).
The basic concept of a “negative index” transmission line, formed by exchanging the shunt capacitance for inductance and the series inductance for capacitance, is shown, for example, in Pozar, Microwave Engineering (Wiley 3d Ed.). The transmission line approach to metamaterials has been explored by Itoh and Caloz (UCLA) and Eleftheriades and Balmain (Toronto). See for example Elek et al, “A two-dimensional uniplanar transmission-line metamaterial with a negative index of refraction”, New Journal of Physics (Vol. 7, Issue 1 pp. 163 (2005); and U.S. Pat. No. 6,859,114.
The transmission lines (TLs) disclosed by Caloz and Itoh are based on swapping the series inductance and shunt capacitance of a conventional TL to obtain the TL equivalent of a negative index medium. Because shunt capacitance and series inductance always exist, there is always a frequency dependent dual behavior of the TLs that gives rise to a “backward wave” at low frequencies and a typical forward wave at higher frequencies. For this reason, Caloz and Itoh have termed their metamaterial TL a “composite right/left handed” TL, or CRLH TL. The CRLH TL is formed by the use of lumped capacitors and inductors, or equivalent circuit elements, to produce a TL that functions in one dimension. The CRLH TL concept has been extended to two dimensional structures by Caloz and Itoh, and by Grbic and Eleftheriades.
Use of a complementary split ring resonator (CSRR) as a microstrip circuit element was proposed in F. Falcone et al, “Babinet principle applied to the design of metasurfaces and metamaterials,” Phys. Rev. Lett. V93, Issue 19, 197401. The CSRR was demonstrated as a filter in the microstrip geometry by the same group. See e.g., Marques et al, “Ab initio analysis of frequency selective surfaces based on conventional and complementary split ring resonators”, Journal of Optics A: Pure and Applied Optics, Volume 7, Issue 2, pp. S38-S43 (2005), and Bonache et al, “Microstrip Bandpass Filters With Wide Bandwidth and Compact Dimensions” (Microwave and Optical Tech. Letters (46:4, p. 343 2005). The use of CSRRs as patterned elements in the ground plane of a microstrip was explored. These groups demonstrated the microstrip equivalent of a negative index medium, formed using CSRRs patterned in the ground plane and capacitive breaks in the upper conductor. This work was extended to coplanar microstrip lines as well.
A split-ring resonator (SRR) substantially responds to an out-of-plane magnetic field (i.e. directed along the axis of the SRR). The complementary SRR (CSRR) , on the other hand, substantially responds to an out-of-plane electric field (i.e. directed along the CSRR axis). The CSRR may be regarded as the “Babinet” dual of the SRR and embodiments disclosed herein may include CSRR elements embedded in a conducting surface, e.g. as shaped apertures, etchings, or perforation of a metal sheets. In some applications as disclosed herein, the conducting surface with embedded CSRR elements is a bounding conductor for a waveguide structure such as a planar waveguide, microstrip line, etc.
While split-ring resonators (SRRs) substantially couple to an out-of-plane magnetic field, some metamaterial applications employ elements that substantially couple to an in-plane electric field. These alternative elements may be referred to as electric LC (ELC) resonators, and exemplary configurations are depicted in D. Schurig et al, “Electric-field coupled resonators for negative permittivity metamaterials,” Appl. Phys. Lett 88, 041109 (2006). While the electric LC (ELC) resonator substantially couples to an in-plane electric field, the complementary electric LC (CELC) resonator substantially responds to an in-plane magnetic field. The CELC resonator may be regarded the “Babinet” dual of the ELC resonator, and embodiments disclosed herein may include CELC resonator elements (alternatively or additionally to CSRR elements) embedded in a conducting surface, e.g. as shaped apertures, etchings, or perforations of a metal sheet. In some applications as disclosed herein, a conducting surface with embedded CSRR and/or CELC elements is a bounding conductor for a waveguide structure such as a planar waveguide, microstrip line, etc.
Some embodiments disclosed herein employ complementary electric LC (CELC) metamaterial elements to provide an effective permeability for waveguide structures. In various embodiments the effective (relative) permeability may be greater then one, less than one but greater than zero, or less than zero. Alternatively or additionally, some embodiments disclosed herein employ complementary split-ring-resonator (CSRR) metamaterial elements to provide an effective permittivity for planar waveguide structures. In various embodiments the effective (relative) permittivity may be greater then one, less than one but greater than zero, or less than zero.
Exemplary non-limiting features of various embodiments include:                Structures for which an effective permittivity, permeability, or refractive index is near zero        Structures for which an effective permittivity, permeability, or refractive index is less than zero        Structures for which an effective permittivity or permeability is an indefinite tensor (i.e. having both positive and negative eigenvalues)        Gradient structures, e.g. for beam focusing, collimating, or steering        Impedance matching structures, e.g. to reduce insertion loss        Feed structures for antenna arrays        Use of complementary metamaterial elements such as CELCs and CSRRs to substantially independently configure the magnetic and electric responses, respectively, of a surface or waveguide, e.g. for purposes of impedance matching, gradient engineering, or dispersion control        Use of complementary metamaterial elements having adjustable physical parameters to provide devices having correspondingly adjustable electromagnetic responses (e.g. to adjust a steering angle of a beam steering device or a focal length of a beam focusing device)        Surface structures and waveguide structures that are operable at RF, microwave, or even higher frequencies (e.g. millimeter, infrared, and visible wavelengths)        